Question

Is root 3 +root 3 a rational number

Answer 1

irrational

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Ideas: You can use indirect proof.

Step 1. Assume sqrt(3) is rational. By definition, sqrt(3) can be written as m/n, where both m and n are positive integers, and m and n are relatively prime.

sqrt(3) = m/n

Step 2. Try to find contradiction.

Square both sides,

3 = m^2/n^2

=> m^2 = 3n^2

=> 3 is a factor of m.

Let m = 3k

=> 9k^2 = 3n^2

=> n^2 = 3k^2

=> 3 is a factor of n.

So, 3 is a factor of both m and n, which is contradictory to the assumption in step 1 that m and n are relatively prime.

Step 3. Therefore, the assumption in step 1 is false. So, sqrt(3) must be an irrational number

Answer 2

Answer:

No, the square root of 3 is not rational. No. The square root of 3 is irrational.. More generally: if p is a prime number then the square root of p. is irrational.